After a turgid 120 minutes the visitors deservedly went through 4-2 on penalties, much to the delight of their 2,000 travelling supporters as they saw their team set up an intriguing semi-final against arch-rivals Falkirk.
The Dons' first attack should have brought the opening goal within only two minutes. Sone Aluko raced onto a Scott Severin pass and, with the visitors' defence in retreat, he drove a great ball into the area where Darren Mackie completely miskicked in front of goal.
On six minutes good interplay between Mackie and Jamie Smith saw the latter drift away from his marker before clipping the ball into the near post where Mark Kerr had timed his run to power in a header which was brilliantly tipped over by the visitors' keeper Paul Gallacher.
The visitors almost shocked their hosts on 18 minutes when Alex Burke's deep cross saw Steven Bell climb above Jamie Langfield but his looping header fell just wide of the upright.
At the other end a deep corner beyond the far post on 25 minutes from Charlie Mulgrew found the head of Alexander Diamond but the centre-back couldn't direct his downward header on target.
Casual play in the Dons defence allowed Burke to carry the ball 20 yards before playing in a great cross which found the head of the unmarked Bell but, with the goal gaping, his headed effort fell straight into the midriff of Langfield.
In a very uneventful restart it took until the 55th minute before either side fashioned an opening. Burke slipped away from Richard Foster before crossing to find the head of Graham Bayne whose ten-yard header looped over the bar.
Aberdeen came close on 65 minutes when a Mulgrew corner caused all sorts of panic in the visitors' rearguard with Scott Wilson finally hacking the ball away from inside his own six-yard box.
The Pars were always dangerous on the break and on 66 minutes Bayne gathered a Burke pass before firing in a right-foot shot which Langfield required two attempts to hold.
Aberdeen thought they had broken the deadlock on 87 minutes. Andrew Considine climbed above Scott Thomson to power in a header which was somehow hooked off the line by Wilson.
There was just enough time for the home side to pass up their best chance of the entire 90 minutes.
Jamie Smith drew the defender before neatly clipping the ball through to Aluko who took a poor first touch before driving the ball beyond Gallacher only for a combination of Wilson and Stephen Glass to clear off the line.
On 105 minutes Smith skipped away from Calum Woods before crossing to the far post where a Tommy Wright header was easily held under the crossbar.
In the end Gallacher was the hero as he saved penalties from Severin and Foster in the shoot-out to send Dunfermline through to the semi-finals.